Sign up to receive free email alerts when patent applications with chosen keywords are publishedSIGN UP

Abstract:

A method of eliminating information on the projection states of projection
elements (P) by using an analysis model in which discharged projection
elements (P) repeatedly collided with rotation blades (13) in a
projection machine having rotating blades (13). The method comprises the
step of determining initial conditions including information on the size
and rotation of blades (13), discharging information on the projection
elements (P), and information on projection elements with respect to the
blades (13) the step of storing the initial conditions, a computing step
of computing the position of each projection element (P), and its
velocity and direction after collision with a blade (13) based on the
initial conditions, and the step of estimating information on projection
state based on computation results.

Claims:

1. A method of estimating information on the state of projection of
abrasive particles projected by a projection machine that includes a
plurality of blades that rotate at a high rate, the method comprising the
steps of:analyzing the behavior of said abrasive particles projected by
said projection machine on said blades to create an analytical model;
andestimating the information on the state of the projection of the
abrasive particles projected by said projection machine using said
analytical model.

2. The method of claim 1, wherein said behavior of each abrasive particle
includes contact with at least one of the other abrasive particles and
one of the rotating blades.

3. The method of claim 1, wherein the information on the state of the
projection of the abrasive particles is at least one of a distribution of
a projection of said abrasive particles and a velocity of a projection of
the abrasive particles.

4. The method of claim 1, wherein said projection machine is a centrifugal
projection machine.

5. A method of estimating information on the state of projection of
abrasive particles projected by a projection machine that includes a
plurality of blades that rotate at a high rate, and an opening through
which the abrasive particles are projected by said blades to an article
to be processed, the method comprising the steps of:determining initial
conditions that include information on a size and a rate of rotation of
said blades, information on the projection of the abrasive particles,
information on the abrasive particles in relation to said blades;storing
said initial conditions;calculating positions of each abrasive particle,
and velocities and directions of the abrasive particles after collisions
with said blades, based on said initial conditions; andestimating the
information on said state of the projection based on the result of said
calculation.

6. The method of claim 4, wherein the information on the state of the
projection of the abrasive particles is at least one of a distribution of
the projection of said abrasive particles and the velocity of a
projection of the abrasive particles.

7. The method of claim 5, wherein said step for calculating
includes:expressing a velocity of each abrasive particle after a
collision as a relative velocity that includes a vertical component along
a Y-axis and a horizontal component along an X-axis using a transfer
vector of the abrasive particle and a transfer vector of the movement of
a point of collision on a surface of the corresponding blade on which the
abrasive particle is impacted, wherein the vertical component of the
relative velocity is expressed as a bounce using the coefficient of
rebound by a determination of a coefficient, and wherein the horizontal
component is expressed as a loss of speed due to a resistance by friction
by a determination of a coefficient; andcalculating a velocity and a
direction of the abrasive particle after a collision with the
corresponding blade by summing them and calculating the transfer vector
of the blade at said collision point.

8. The method of claim 5, wherein said step for calculating
includes:calculating a magnitude of a force of the contact of each
abrasive particle relative to at least one of the blade and another
abrasive particle; andcalculating an acceleration of the abrasive
particle based on forces that act on the abrasive particle that include
said force of the contact and gravity, and obtaining data on a velocity
and a position of the abrasive particle after a minimal time based on the
calculated acceleration.

9. The method of claim 4, wherein said step of calculating the
acceleration calculates the distance that the abrasive particle moves and
the distance the corresponding blade moves in a sampling time, and
executes the calculation relating to the collision of an abrasive
particle that complies with sequential conditions for collisions.

10. The method of claim 4, wherein the method further includes the step of
displaying the result of said calculation.

11. The method of claim 4, wherein said projection machine is a
centrifugal projection machine.

12. The method of claim 4, wherein the method further includes the step of
adjusting a profile of the distribution of the projection of the abrasive
particles to a predetermined profile by selecting values of the
dimensions of each blade, the range of positions of projection on the
opening from which the abrasive particles are projected, and a rate of
rotation of the blade such that a variability of the frequency to which
each discharged abrasive particle rebounds from the blade is a
predetermined value or less.

13. The method of claim 10, wherein the predetermined value is 0.3.

14. The method of claim 11, wherein the range of positions for the
projection on the opening from which the abrasive particles are projected
is 5.degree. to 20.degree..

15. The method of claim 10, wherein the values of the dimensions include a
ratio of the inner diameter and the outer diameter of the blade, wherein
the range of this ratio is any one of 1.75 to 2.0, 2.5 to 2.9, and 3.6 to
4.1.

16. A system with a programmed computer for estimating information on the
state of projection of abrasive particles projected by a projection
machine that includes a plurality of blades that rotate at a high rate,
said computer comprising:a) input means for providing initial conditions
that include information on the size and rotation of said blades,
information on the projection of the abrasive particles, information on
the abrasive particles in relation to said blades and to said computer;b)
calculating means for calculating a position of each abrasive particle,
and velocities and directions of the abrasive particles after collisions
with said blades, based on said initial conditions;c) means for
estimating the information on said state of the projection based on the
result of said calculation; andd) means for displaying said presumed
information.

17. The system of claim 16, wherein said calculating means calculates a
magnitude of a force of the contact of each abrasive particle relative to
at least one of the blade and other abrasive particles, and calculates an
acceleration of the abrasive particle based on forces that act on the
abrasive particle that include said force of the contact and gravity, and
obtaining a velocity and a position of the abrasive particle after a
minimal time based on the calculated acceleration.

18. The system of claim 16, wherein said computer further includes a
storage medium in which a program for a calculation to be executed by
said calculation means is stored.

19. The system of claim 16, wherein said calculating means expresses a
velocity of each abrasive particle after a collision as a relative
velocity that includes a vertical component along a Y-axis and a
horizontal component along an X-axis using a transfer vector of the
abrasive particle and a transfer vector of a point of collision on a
surface of the corresponding blade on which the abrasive particle
impacts, wherein the vertical component of the relative velocity is
expressed as a bounce using the coefficient of rebound by a determination
of a coefficient, and wherein the horizontal component is expressed as a
loss of speed caused by a resistance for friction by a determination of a
coefficient determination; andwherein said calculating means calculates a
velocity and a direction of the abrasive particle after a collision with
the corresponding blade by summing them and calculating the transfer
vector of the blade at said collision point.

20. The system of claim 16, wherein said calculating means calculates a
distance the abrasive particle moves and the distance the corresponding
blade moves in a sampling time, and executes the calculation relating to
the collision for an abrasive particle that complies with sequential
crash condition.

21. The system of claim 14, wherein said projection machine is a
centrifugal projection machine.

22. The system of claim 14, wherein a profile of the distribution of the
projection of the abrasive particles is adjusted to a predetermined
profile by selecting values of the dimensions of each blade, the range of
positions of projection on the opening from which the abrasive particles
are projected, and a rate of rotation of the blade such that a
variability of the frequency to which each discharged abrasive particle
rebounds for the blade is a predetermined value or less.

23. The system of claim 19, wherein the predetermined value is 0.3.

24. The system of claim 20, wherein the range of positions of the
projection on the opening from which the abrasive particles are projected
is 5.degree. to 20.degree..

25. The system of claim 10, wherein the values of the dimensions include a
ratio of the inner diameter to the outer diameter of the blade, wherein
the range of this ratio is any one of 1.75 to 2.0, 2.5 to 2.9, and 3.6 to
4.1.

26. A method aided by a programmed computer for controlling a projection
of abrasive particles to be projected to an article by a projection
machine that includes a plurality of blades that rotate at a high rate,
and for estimating information on the state of said projection of said
abrasive particles, the method comprising the steps of:a) entering
information on the blade, a condition of projection of the abrasive
particles, and a coefficient of bounce and a coefficient of resistance to
friction of the abrasive particle, in said computer;b) determining by
said computer whether said entering in said entering step is completed,
and calculating by said computer positions of respective abrasive
particles per a given sampling time based on the sampling time and a
transfer vector of the abrasive particle, if said entering is
completed;c) turning the blades by said computer to update the angles of
the blades;d) determining by said computer whether each abrasive particle
impacts the corresponding blade, calculating by said computer a velocity
and a direction of the impacted abrasive particle to update the transfer
vector of the abrasive particle, if said computer determines that the
abrasive particle impacts the corresponding blade, while maintaining the
transfer vector, if said computer determines no abrasive particle impacts
the corresponding blade;e) determining by said computer whether a
position of said blades is within a range from which the abrasive
particles are discharged, discharging the abrasive particles, if the
position of said blades is within the range of discharge of the abrasive
particles, while preventing the abrasive particles from being discharged,
if the position of said blades is outside the range of discharge of the
abrasive particles,f) determining by said computer whether the positions
of the blades has been turned to the predetermined positions, totaling
the transfer vectors of respective abrasive particles, if said
determination indicates that the positions of the blades have been turned
to the predetermined positions, while repeating steps b) to f), if said
determination indicates that the positions of the blades has not been
turned to the predetermined position; andg) displaying by said computer
the distribution of the projection and the velocity of the projection and
of the result of the calculations for the total.

Description:

FIELD OF THE INVENTION

[0001]This invention generally relates to a method and a system for
estimating information on projection conditions for projecting abrasive
particles by a projection machine. More particularly, this invention
relates to a method and a system that enables information to be estimated
on the conditions of the projection without a trial for manufacturing
parts of the projection machine.

BACKGROUND OF THE INVENTION

[0002]In a surface-treatment device such as a shot-peening machine, it is
preferable to set optimal projection conditions of abrasive particles to
be projected by a projection device based on the shape of an article to
be processed and the area of the surface to be processed, etc. The
projection conditions of the abrasive particles in this context include
the area to be shot-peened or the distribution of the shot-peening, as
well as the amount and the velocity of the abrasive particles to be
projected. To this end, Japanese Patent Early-Publication No. 1996-323629
(prior art 1), by the assignor of the present application, discloses a
method and an apparatus for regulating the distribution of the shot
peened based on the article to be processed when the quantity and the
velocity of the abrasive particles to be projected are changed based on
that article to be processed.

[0003]As another prior-art publication, a shot-peening machine is
disclosed in Japanese Patent Early-Publication No. 1989-264773 (prior art
2). It limits the distribution of the shot peened by projecting the
abrasive particles of the shot peened in a distribution that is wider
than the surface to be processed and by providing a so called vane as a
liner between the projection device and the article to be processed, to
limit the range of the projection of the abrasive particles.

[0004]Further, the apparatus disclosed in Japanese Patent
Early-Publication No. 2003-340721(prior art 3) is configured to
concentrate the distribution of the abrasive particles within a
predetermined range by shortening the length of a blade so as to maintain
the constant direction of the projection without using a vane.

[0005]However, in the disclosures of prior art 1, deciding the
distribution and the velocity of the projection necessitates a
centrifugal projecting device that actually projects the abrasive
particles to the article to be processed to confirm the distribution and
the velocity of the abrasive particles based on the result of the actual
projecting. Therefore, it necessitates time to obtain an accurate
relationship between the optimum processing and the distribution of the
projection. Desirably, the centrifugal projecting device will provide for
distribution of the projection that is best suited for articles to be
processed and for the processing method in the centrifugal projection
device, because saving energy and an efficient projection are needed.
From this viewpoint, it is inconvenient to require time to understand an
accurate relationship between the optimum processing and the distribution
of the projection.

[0006]Moreover, because the vane is worn out by the collisions with the
abrasive particles, thus a vane that restricts the range of the
projection may change this range in the device of prior art 2. So it
might cause the quality of the articles for processing to decrease.
Therefore, it is frequently necessary to exchange a vane. Moreover,
because the abrasive particle is reflected from the vane, and the
particle rebounds in the inner wall of the projection chamber, the
protection from wear from the wall of the projection chamber is also
necessary.

[0007]In contrast, in the device of prior art 3 the difference is caused
at the position of the blade where the supply of the abrasive particles
is not constant, each part of the abrasive particles collides, and the
distribution of the projection diffuses though the length of the blade
and is extremely shortened, to concentrate the distribution of the
projection to a predetermined range. Therefore, it is easy to receive the
effect when the supply of the abrasive particles is unstable. Moreover,
the slower the velocity is of the rotation of the impeller, possibly the
efficiency of the treatment decreases, because abrasive particles that
are dispersed outside of the impeller without colliding with the blade
are generated. In addition, because it greatly affects the accuracy of
the distribution of the projection when the shape of the blade changes by
the wear, and because the blade is worn out by the collisions with the
abrasive particles, it is necessary to frequently exchange the blades.

[0008]Accordingly, one object of the present invention is to provide a
method and a system for estimating information on the state of the
projection of abrasive particles projected by a projection machine to
reduce operating costs and the time to know conditions involving the
state of the projection of the abrasive particles to define information
on a specified state, e.g., at least the distribution of the projection
or the velocity of the projection.

SUMMARY OF THE INVENTION

[0009]One aspect of the present invention provides a method of estimating
information on the state of the projection of abrasive particles
projected by a projection machine that includes a plurality of blades
that rotate at a high rate. The method comprises the steps of analyzing
the behavior of the abrasive particles projected by the projection
machine on the blades, to create an analytical model, and estimate the
information on the state of the projection of the abrasive particles
projected by the projection machine using the analytical model.

[0010]The action of each abrasive particle includes contact with at least
one other abrasive particle and one of the rotating blades.

[0011]Another aspect of the present invention provides a method of
estimating information on the state of the projection of abrasive
particles projected by a projection machine that includes a plurality of
blades that rotate at a high rate, and an opening through which the
abrasive particles are projected by the blades to an article to be
processed. The method comprises the steps of determining the initial
conditions. They include information on the size, and the rate of the
rotation of, the blades, information on the projection of the abrasive
particles, information on the abrasive particles in relation to the
blades; storing the initial conditions; calculating the positions of each
abrasive particle, and the velocities and directions of the abrasive
particles after collisions with the blades, based on the initial
conditions; and estimating the information on the state of the projection
based on the result of the calculation.

[0012]The result of the calculation may be displayed.

[0013]Yet another aspect of the present invention provides a system with a
programmed computer to estimate information on the state of the
projection of the abrasive particles projected by a projection machine
that includes a plurality of blades that rotate at a high rate. The
computer comprises a) input means for providing to the computer initial
conditions that include information on the size and rotation of the
blades, information on the projection of the abrasive particles,
information on the abrasive particles in relation to the blades; b)
calculating means for calculating the position of each abrasive particle,
and the velocities and directions of the abrasive particles after
collisions with the blades, based on the initial conditions; c) means for
estimating the information on the state of the projection based on the
result of the calculation; and d) means for displaying the assumed
information.

[0014]In one embodiment of the present invention, the calculating means
calculates the magnitude of a force of contact of each abrasive particle
relative to at least one of the blades and the other abrasive particles;
and calculates the acceleration of the abrasive particle based on the
forces that act on it. They include the force of the contact and the
gravity, and obtaining the velocity and the position of the abrasive
particle after a short time, based on the calculated acceleration.

[0015]The computer may further include a storage medium in which a program
for calculation to be executed by the calculation means is stored.

[0016]The calculating step and the calculating means in the method of the
second aspect and the system of the third aspect of the present invention
express the velocity of each abrasive particle after a collision as a
relative velocity that includes a vertical component along a Y-axis and a
horizontal component along an X-axis using the transfer vector of the
abrasive particle and the transfer vector of the point of collision on a
surface of the corresponding blade on which the abrasive particle is
impacted, wherein the vertical component of the relative velocity is
expressed by a bounce that uses the coefficient of the rebound by a
determination of a coefficient, and wherein the horizontal component is
expressed as a loss of velocity due to resistance from friction by a
determination of a coefficient; and calculates the velocity and the
direction of the abrasive particle after a collision with the
corresponding blade by summing them plus calculating the transfer vector
of the blade at the point of the collision. In this case, the step for
calculating, or the calculating means, may calculate the distance the
abrasive particle moves and the distance the corresponding blade moves in
a sampling time, and executes the calculation relating to the collision
for an abrasive particle that complies with sequential conditions of
collisions.

[0017]The method of the system of another aspect of the present invention
may adjust a profile of the distribution of the projection of the
abrasive particles to a predetermined profile by selecting the values of
each blade, the range of the positions of the projections on the opening
from which the abrasive particles are projected, and the rate of rotation
of the blade such that the variability of the frequency to which each
discharged abrasive particle rebounds from the blade is a predetermined
value or less. Preferably, the predetermined value is 0.3.

[0018]The values of the dimensions include a ratio of the inner diameter
and the outer diameter of the blade, the range of this ratio preferably
being any one of 1.75 to 2.0, 2.5 to 2.9, and 3.6 to 4.1.

[0019]In the above aspects of the present invention, the information on
the state of the projection of the abrasive particles is at least either
a distribution of the projection of the abrasive particles or the
velocity of the projection of the abrasive particles. The projection
machine may, for instance, be a centrifugal projecting device.

[0020]The present invention further provides a method aided by a
programmed computer for controlling the projection of abrasive particles
to be projected to an article by a projection machine that includes a
plurality of blades that rotate at a high rate, and for estimating
information on the state of the projection of the abrasive particles. The
method comprises the steps of a) entering information on the blade, the
condition of the projection of the abrasive particles, and the
coefficient of bounce and the coefficient for the resistance to friction
of the abrasive particle to the computer; b) determining by the computer
whether entering the entering step has been completed, and calculating by
the computer positions of respective abrasive particles per a given
sampling time based on the sampling time and the transfer vector of the
abrasive particle, if the entering is completed; c) turning the blades by
the computer to update the angles of the blades; d) determining by the
computer whether each abrasive particle impacts the corresponding blade,
calculating by the computer the velocity and the direction of the
impacted abrasive particle to update the transfer vector of the abrasive
particle, if the computer determines the abrasive particle impacts the
corresponding blade, while maintaining the transfer vector, if the
computer determines no abrasive particle impacts the corresponding blade;
e) determining by the computer whether the position of the blades is
within a range from which the abrasive particles are discharged,
discharging the abrasive particles, if the position of the blades is
within the range from which the abrasive particles are discharged, while
preventing the abrasive particles from being discharged, if the positions
of the blades are outside the range from which the abrasive particles are
discharged,

[0021]f) determining by the computer whether the positions of the blades
have been turned to the predetermined positions, totaling the transfer
vectors of the respective abrasive particles, if the determination
indicates that the positions of the blades have been turned to the
predetermined positions, while repeating steps b) to f), if the
determination indicates that the positions of the blades have not turned
to the predetermined position; and g) displaying by the computer the
distribution of the projection and the velocity of the projection and of
the result of the calculations for the total.

[0022]The above and other scopes and advantages of the present invention
will become apparent by reviewing the following detailed description with
reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023]FIG. 1 shows a cross-sectional view of an essential part of a
centrifugal projecting device to illustrate one example of a projection
machine to which the present invention can be applied.

[0024]FIG. 2 schematically illustrates the action of an abrasive particle
on a blade.

[0025]FIG. 3 is a vector diagram that shows velocities of the abrasive
particle before and after the collisions with the blades.

[0026]FIG. 4 schematically illustrates factors that contribute to the
initial condition in an analytical model.

[0027]FIG. 5 is a vector diagram that shows the velocity of an abrasive
particle after it collides.

[0028]FIG. 6 is a flowchart of one embodiment of the method of the present
invention.

[0029]FIG. 7 shows an example of displaying the result of the calculation
in the embodiment of FIG. 6.

[0030]FIG. 8 is a graph of the calculation of the projection E1 of a
distribution in conjunction with an actual distribution of the projection
E.

[0031]FIG. 9 is a graph of the relationship between the outer diameter and
the average velocity of the projection when the velocity of the
circumference is constant.

[0032]FIG. 10 is a schematic block diagram of one example of a computer
used for the system to execute the method of the present invention.

[0033]FIG. 11 is a flowchart of another embodiment of the method of the
present invention.

[0034]FIG. 12 illustrates one example of finding a force of the contact
between the abrasive particles in the model for the analysis of movement.

[0035]FIG. 13 shows an example of displaying the result of the calculation
in the embodiment of FIG. 12.

[0036]FIG. 14 is a graph of the relationship between variability of the
frequency of the rebounding of the abrasive particle and a variability of
a direction of the projection of the abrasive particle.

[0037]FIG. 15 is a graph of the relationship between a mean frequency of
the rebounding of the abrasive particle and a variability of a direction
of the projection of the abrasive particle.

[0038]FIG. 16 is a graph of the distribution of the projections shown by
different ranges of the positions from which the abrasive particles are
discharged.

[0039]FIG. 17 is a graph of the variability of a direction of the
projection of an abrasive particle projection while the ranges of the
positions from which the abrasive particles are discharged are varied.

[0040]FIG. 18 is a graph of the relationship between the proportion of the
outer diameter relative to the inner diameter, a variability of a
frequency of the rebounding of the abrasive particle, and a variability
of a direction of the projection of the abrasive particle.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041]One embodiment of the present invention that is applicable to a
centrifugal projecting device that projects centrifugally will now be
explained. The machine that projects centrifugally is a projection
machine that includes an impeller having a plurality of blades and a
cylindrical control cage arranged in the interior of the impeller.
Abrasive particles are impelled through an opening of the control cage
and are projected to an article to be processed by rotating the impeller
at a high rate. However, this invention is not limited to such a machine
that projects centrifugally.

[0042]First, an initial experiment is carried out to investigate the
action of one abrasive particle freely released from the control cage of
the machine that projects centrifugally at one rotating blade. In the
initial experiment, the action of the abrasive particle on the blade was
evidenced using an impact paper.

[0043]As shown in FIG. 1, the machine that projects centrifugally that is
used for the initial experiment includes a housing (an impeller casing) 2
mounted on an upper wall 1 on the ceiling of the protecting cavity of the
main unit of the project machine, a driving mechanism 3 on the upper wall
1 on the outside of a first sidewall 2a of the housing 2, and an impeller
4 mounted on a shaft 3a for driving the driving mechanism 3. The
centrifugal projecting device further includes a distributor 5 coaxially
mounted on the driving shaft 3a in the inner peripheral space S in the
impeller 4 to stir the abrasive particles, a cylindrical control cage 6
mounted on a second sidewall 2b which is opposed to the first sidewall 2a
of the housing 2, to restrict the direction in which the abrasive
particles are projected, and a feed cylinder 7, mounted on the second
sidewall 2b of the housing 2.

[0044]The impeller 4 is mounted on the driving shaft 3a with a bolt 11
through a hub 10. The impeller 4 comprises a first shroud 12a at the side
of the driving shaft 3a of the driving mechanism 3a, a second shroud 12b
in a position that is spaced apart from the first shroud 12a and toward
the feed cylinder 7, and further comprises a plurality of blades 13 that
are fixedly sandwiched between the first shroud 12a and the second shroud
12b such that they are arranged radially.

[0045]The distributor 5 is fixed to the first shroud 12a with a bolt 14.
The distributor 5 is provided with openings (cutouts) arranged in its
circumference at substantially equal intervals. The number of openings 15
may be equal to, or be more than, or less than, that of the blades 13.

[0046]On the control cage 6, a cylindrical portion of its distal end is
provided with an equiangular window 17 to restrict the direction in which
the abrasive particles are projected. The control cage 6 is mounted on
the housing 2 at the side of the second shroud 2b such that it extends
between the distributor 5 and the blades 13.

[0047]FIG. 2 illustrates the action of an abrasive particle P on the blade
as a result of the initial experiment. The result of the behavior of the
abrasive particle P on the blade can be assumed to be a rebound
phenomenon of the blade, rather than a sliding motion on the blade,
because pressures are concentrated at two or three positions on the
blade. Namely, the abrasive particle P supplied by the feed cylinder of
the centrifugal projecting device is stirred by the rotating distributor
5 and is then discharged from the opening 17 of the control cage 6 to the
outer periphery of the base of the rotating blade 13. The abrasive
particle P is then accelerated and made to rebound on the blade 13 to
project the abrasive particle P to the distal end (the outer periphery)
of the blade 13.

[0048]This means that an analytical model of the distribution of a
projection can be expressed using an analytical model of the rebound
phenomenon of the abrasive particle P.

[0049]Consequently, the vector components of the velocity of the abrasive
particle after it has collided are divided into relative velocities (V0x,
V0y, V1x, V1y) on the X-axis and the Y-axis using a V0 of the abrasive
particle P, and a transfer vector V1 of the abrasive particle P from the
point of the collision on the surface of the blade.

[0050]The vertical component V1y may be expressed as a bounce using the
coefficient of rebounding. The horizontal component V1x may be expressed
as a loss of velocity by a resistance caused by friction. Therefore, the
following equations (1-1) and (1-2) can be obtained by introducing their
respective coefficients.

V1y=-eV0y (1-1)

V1x=(1-μ)V0x (1-2)

[0051]where e is the coefficient of rebounding, and μ is the
coefficient of the resistance to friction.

[0052]Initial conditions for the analytical model of the distribution of
the projection may include, e.g., information on the dimensions and the
rotation of the blade (hereafter, "blade information") that corresponds
to various conditions of a real machine, and information on the
projection of the abrasive particle from the control cage. For instance,
assignable factors, e.g., an outer diameter, an inner diameter, a length,
the width of a blade, the number of blades, and a velocity of rotation
(velocity of the rotation of an impeller) can be considered in the
initial conditions. As shown in FIG. 4, a range (angle α) of the
discharge of the abrasive particles P from the opening 17 of the control
cage 6, a direction of the projection of the abrasive particles, an
initial rate, and the variation of the range of the abrasive particles P,
can also be considered in the initial conditions. The range of the
discharge corresponds to a range where the abrasive particles P are
discharged from the control cage 6. It can be represented as an angle,
and determined based on the shape of the opening 17 and the shape of the
distributor 5 (not shown in FIG. 4). Further, the range of the variation
corresponds to the direction from where the abrasive particles P are
projected from the control cage 6 and the range of distribution of the
initial rate. Because the range of the distribution varies based on the
shape of the opening 17 of the control cage 6 and the shape of the
distributor 5, it may be given as a rectangular distribution, in which
the degree of probability is constant within the range of the variations,
or may be given as the normal distribution by providing a standard
deviation as the range of variations. To determine the coefficient of
bounce and the coefficient of the resistance to friction for the
analytical model, an actual coefficient of bounce is calculated from the
result of a measurement of the amount of the bounce of the abrasive
particles P on the blade 13 by using actual abrasive particles P and the
blade 13. Further, an adequate combination was selected and assigned by
collating the result of the measurements of the distribution of the
projection and the projection rate by an actual projection examination
and the result of a calculation of a distribution of the projection.

[0053]In the analytical model, a calculation is carried out for any of the
blades 13 that accelerates the abrasive particles under the above initial
conditions and the assumption that each blade is symmetrical with respect
to a point. Information that comprises the direction of the projection, a
position, and a velocity is given to the respective abrasive particles P
to calculate a distance for the abrasive particles P and the blade 13
over the time of a sampling, which is preferably 100μ or less, as,
say, to consider the accuracy of the calculation. The calculation of the
collision of the abrasive particles P that complies with the crash
conditions is then carried out sequentially. The positions of the
abrasive particles P are thus denoted by polar coordinates (ra,
θa). It is assumed that where the angle is θb on the surface,
which angle corresponds to a radius diameter ra of the blade, and it is
greater than the angle θa for each abrasive particle P, there is a
collision. Then the expressions (1-1) and (1-2) in the vertical component
and the horizontal component, respectively, which are based on the
surface of the blade as a reference, are obtained. As shown in FIG. 5,
the resulting transfer vector (actual transfer vector of the abrasive
particle) for the abrasive particle on the point of collision on the
blade 13 is on the sum of a transfer vector at the point of collision for
the blade 13 plus a relative transfer vector for the abrasive particle.
The velocity and the direction of the abrasive particle P by the
collision with the blade 13 are then recalculated using the above
resulting vector (the calculation of the collision is repeated). While
not mandatory for the present invention, the results of the analysis
after this calculation may be displayed on a touch screen on a system
that is equipped with a computer commonly having a calculation function
and a display function, or a display screen such as a display on a
control panel.

[0054]One example of the method of estimating information on the state of
a projection of the present invention is shown in the flowchart of FIG.
6. One example of the system that executes the method is schematically
illustrated in FIG. 10. A system 20, shown in FIG. 10, is a
general-purpose computer in which an input device (input means) 22, which
may include a keyboard and mouse, an internal or external data-storing
medium 24 for storing data, an internal or external program-storing
medium 26 for storing programs, a CPU (estimating means), a calculation
unit (calculating means) 30 that includes, e.g., an arithmetic processor
associated with the CPU 28, and a display (display means) 32, are all
connected by a bus line 34. The display 32 may be a touch screen to be
combined with the input device. The programs to execute the method of the
present invention, such as a calculating program, etc., to be executed by
the calculation unit 30, are stored in the program-stored medium 26.

[0055]By referring to the flowchart of FIG. 6, one embodiment to execute
the method of estimating information on the state of the present
invention with a general-purpose computer 20 will now be explained.

[0056](1) First, data on the outer diameter, the inner diameter, the
number, and the velocity of the rotation of the blades 13 are entered
into the data storage medium 24 of the computer 20 as the blade
information used in the analytical model of the distribution of the
projection (step S1). As input values in step S1, say, the outer diameter
is 360 mm, the inner diameter is 135 mm, the number of blades 13 is 8,
and the rate of the rotation is 3,000 rpm.

[0057](2) The range of the discharge of the abrasive particles P (angle),
the direction where the abrasive particles are discharged, the initial
rate, and their variations, are then entered in the data storage medium
24 as the information on the discharge from the control cage 6 (step S2).
As input values in step S2, for instance, the range of the discharge is
35°, the direction is 90° from the position of the
projection to the rotation of the direction, its variation is
±15°, the initial velocity is 10 m/s, and its variation is
±5 m/s.

[0058](3) The coefficient of bounce and the coefficient of the resistance
to friction resistance are then temporarily entered in the data storage
medium 24 (step S3). As input values in step S3, for instance, the
coefficient of bounce is 0.2, and the friction resistance coefficient is
0.6. The inputs in these steps S1, S2, and S3 into the data storage
medium 24 of the computer 20 are carried out through the input device 22.

[0059](4) The CPU 28 determines whether the input has been completed (step
S4).

[0060](5) If the input is completed in step S4, the calculation unit 30
calculates the position of each abrasive particle per a sampling time 80
μs based on the sampling time and the transfer vector (step S5).
Specifically, assuming the position of any abrasive particle at time t is
(X, Y), the following distance (Δx, Δy) of the abrasive
particle after the sampling time Δt can be obtained as
Δx=Vx×Δt and Δy=Vy×Δt based on the
transfer vector (Vx, Vy) of the abrasive particle. Further, the position
of the abrasive particle at time t+Δt can be obtained as
(X+Δx, Y+Δy).

[0061](6) The CPU28 then turns the blade 13 to update its angle (step S6).

[0062](7) The CPU28 then determines whether each abrasive particle P has
collided with the blade 13 (step S7).

[0063](8) If the determination in step S7 has determined that there was a
collision, the calculation unit 30 calculates the velocity and the
direction of the collided abrasive particle to update the transfer vector
(step S8).

[0064]Specifically, the position (X,Y) of the abrasive particle is
converted to the polar representation (ra, θa). If the angle
θb of the surface of the blade 13 that corresponds to the radius ra
is greater than the angleθa of the abrasive particle, a collision
is considered to have occurred. The above equations (i) and (ii), for the
vertical component and the horizontal component, both refer to the
surface of the blade as the reference surface. They are then calculated.
By summing them and the transfer vector for the blade 13 at the point of
collision on the blade, the actual transfer vector for the abrasive
particle is then obtained. The velocity and the direction of the abrasive
particle P by the collision with the blade 13 are then calculated.

[0065]If the determination in step S7 determines that no collision
occurred, the transfer vector of the abrasive particle P is not updated.

[0066](9) The CPU28 then determines whether the position of the blade 13
is within the range of the discharge of the abrasive particle P (step
S9).

[0067](10) If the position of the blade 13 is within the range of the
discharge of the abrasive particle P in step S9, the CPU28 causes the
abrasive particles P to be discharged (step S10). The discharge of the
abrasive particles P means that the abrasive particles are stirred by the
distributor 5 and are discharged from the opening 17 of the control cage
6, and to be discharged into the blade 13 at any time during a process
for an article to be processed.

[0068]The reason it is necessary to determine whether the position of the
blade 13 is within the range of the discharge of the abrasive particle in
step S9 is the following: Because, as discussed above, the calculation is
carried out for any of the blades 13 that comprise the impeller, it
should prevent the abrasive particle P from being discharged when the
discharged abrasive particle P is unsuitable for the analysis because of
the position of the blade 13 (say, where the rotation of the blade 13
advances such that it passes through the opening 17 of the control cage
6).

[0069](11) If the position of the blade 13 is not within the range of the
discharge of the abrasive particle P in step S9, the CPU 28 displays the
result of the calculation of the current state of the projection on the
display 32 (step S11). Typically, 100 to 200 abrasive particles P may be
displayed in this step, although it depends on the arithmetical capacity
of the computer to be used. FIG. 7 shows an example of the display of the
result of this calculation. In this example, the display of the initial
condition is omitted.

[0070](12) The CPU 28 determines whether the position of the blade 13 has
been rotated to a predetermined position. If not, steps S5 to S12 are
repeated to sequentially calculate the positions of the respective
abrasive particles, and the angle of the blade and the transfer vector
for the abrasive particle, after the following sampling time (step S12).

[0071](13) If the determination in step S12 determines that the position
of the blade 13 has been rotated to the predetermined position, the
transfer vectors of respective abrasive particles P are totaled (step
S13).

[0072](14) The distribution of the projection and the velocity of the
projection of the result of the calculations for the total are displayed
(step S14).

[0073]It is recognized that the computed distribution of the projection E1
is close to the actual distribution of the projection E, as shown in FIG.
8.

[0074]The distribution of the projection and the velocity of the
projection of the abrasive particles P from the blade 13 are the
following. The distribution of the projection (the ratio of the number of
projected abrasive particles per 1°) is one wherein the directions
of the transfer vectors of the respective abrasive particles P are
described by angles, and are shown by a histogram. The velocity of the
projection is the calculated mean values of the lengths of the transfer
vectors. The variation in the velocity of the projection is the
calculated standard variability.

[0075]Sequentially, a test is carried out to establish the variation in
the velocity of the projection caused by the outer diameter of the blade
13. As shown in FIG. 9, the actual measured values are very close to the
calculated values (designated by a broken line).

[0076]With this embodiment, the information on the status of the
projection, which includes the distribution of the projection, the
velocity of the projection, and the variation in the velocity of the
projection of the abrasive particles P, can be assumed by using the above
model for an analysis of movements. Therefore, the necessary and various
design conditions (for instance, the length, the shape, the number, and
the rate of the rotation of the blade, and the shape of the opening 17 of
the control cage 6) to know information on the predetermined state of the
projection, can all be determined by adding any required modification to
the initial conditions without actually making them for trial purposes.
In the prior art, pre-producing the blade and the control cage both meant
that the state of the projection had to be repeated by varying their
design conditions, to decrease the necessary design conditions to compile
the information on the predetermined state of the projection. To the
contrary, the cost of the work and the time required to decrease the
necessary design conditions can be reduced in the method and the system
of the present invention, since neither a blade nor a control cage
requires its prototype being manufactured to compile the information of
the state of the predetermined projection.

[0077]By referring to the flowchart of FIG. 11, another embodiment to
execute the method for estimating the information on the conditions of
the projection of the present invention with the general-purpose computer
20 will be explained.

[0078](1) First, data on the outer diameter, the inner diameter, the
number, and the velocity of rotation of the blades 13 are entered in the
data storage medium 24 of the computer 20 as the information on the blade
for the analytical model of the distribution of the projection. Data on
the particle size and the density of the abrasive particle, the amount of
the abrasive particles to be discharged, the range of the discharge of
the abrasive particles P (angle), the direction where the abrasive
particles are discharged, the initial rate, and their variations, are
then entered in the data storage medium 24 as the information on the
discharge from the control cage 6. Further, a coefficient of bounce and a
coefficient of resistance to friction are temporarily entered in the data
storage medium 24 (step S31). The inputs in this step S31 into the data
storage medium 24 are carried out through the input device 22. As input
values for the blade 13 to be entered, for instance, the outer diameter
may be 360 mm, the inner diameter may be 135 mm, the number of blades 13
may be 8, and the rate of the rotation may be 3,000 rpm. As input values
for the abrasive particle to be entered, the particle size in the
diameter may be 1 mm, the density may be 7850 Kg/m3, the amount of
the abrasive particles to be discharged may be 200 kg/min, the range of
the discharge of the abrasive particles may be 35°, the direction
may be 90° from the position of the projection to the rotation of
the direction, its variation may be ±15°, the initial velocity
may be 10 m/s, and its variation may be ±5 m/s. The coefficient of
bounce to be entered may, e.g., be 0.2, and the coefficient of resistance
to friction to be entered may, e.g., be 0.6. These input values are just
examples, and thus are not to limit the present invention.

[0079](2) The CPU 28 then turns the blade 13 to the following position
during a minimal time (for instance, a sampling time Δt=80 μs
after time t=0) (the steps S32, S33, and S34).

[0080](3) The CPU 28 then determines whether each abrasive particle
contacts other movable bodies, based on the calculation of the
calculation unit 30. If the CPU 28 determines there is a contact, it
executes an analysis of the force of the contact acting on each abrasive
particle for all the abrasive particles (step S35). The term "other
movable body" refers to the blade 13 and other abrasive particles. If the
abrasive particle and the other abrasive particle as the other movable
body are in contact with each other with each other, the force that acts
between these abrasive particles are calculated based on the distance
between any abrasive particle i and an abrasive particle j that comes in
contact with the abrasive particle i, to determine whether the abrasive
particles come in contact. If the abrasive particle i and the abrasive
particle j have come in contact, then, based on this result of the
determination, a vector that is oriented from the center of the abrasive
particle i to the center of the abrasive particle j is defined as the
"normal vector," and a vector that is oriented to the direction that is
turned 90° clockwise of the normal vector is defined as a "tangent
vector."

[0081]As shown in FIG. 12, assume virtual and parallel arrangements where
each arrangement includes a spring and a dashpot in the normal direction,
and where the direction of tangent of the abrasive particles i, j is
between the two abrasive particles (discrete elements) i, j that come in
contact with each other, to calculate the force of the contact that is
exerted from the abrasive particle j to the abrasive particle i. The
force of the contact is calculated by the calculation unit 30 as a
resultant force resulting from adding the component of the normal
direction of the force of the contact to the component of the direction
of tangent of the force of the contact.

[0082]In step S35, first, the component of the normal direction of the
force of the contact is calculated for all abrasive particles. Using an
increment of an elasticity resistance, and the spring constant in the
elasticity spring proportional to the amount of contact, the relative
displacement of the abrasive particle i and the abrasive particle j over
a short time can be expressed as

Δen=knΔxn (1)

[0083]where Δen: increment of an elasticity resistance,
[0084]kn: the spring constant in the elasticity spring proportional
to the amount of contact, and [0085]Δxn: the relative
displacement of the abrasive particle i and the abrasive particle j over
a short time.The suffix n denotes a component of the normal direction.

[0086]Using a coefficient of viscosity of the viscous dashpot proportional
to the velocity of the relative displacement, a viscosity resistance
coefficient is given by

Δdn=ηnΔxn/Δt (2)

[0087]where Δdn: an increment of an elasticity resistance, and

kn: the spring constant in the elasticity spring is proportional to
the force of contact.

[0088]The elasticity resistance and the viscosity resistance that are
associated with the component of the normal direction of the force that
acts on the abrasive particle i from the abrasive particle j at a given
time t can be expressed by equations (3) and (4).

[en]t=[en]t-Δt+Δen (3)

[dn]t=Δdn (4)

where [en]t refers to en at the time t.Therefore, the
component of the normal direction of the force of the contact can be
expressed by the following equation (5).

[fn]t=[en]t+[dn]t (5)

where [fn]t is the component of the normal direction of the
force of the contact at the time t.

[0089]Accordingly, the force of the contact that acts on the abrasive
particle i at the time t will be calculated by considering the force of
the contact from all abrasive particles.

[0090]The component of the direction of tangent of the force of contact of
all the abrasive particles is calculated at the end of step S35. It is
considered that in the component of the direction of tangent, the
elasticity resistance is proportional to a relative displacement and to a
velocity of the relative displacement of viscous resistance that is
similar to the component of the normal direction, and thus can be
calculated by the following equation (6).

[ft]t=[et]t+[dt]t (6)

where ft is the component of the direction of direction of tangent of
the force of the contact, et is the component of the direction of
tangent of the elasticity resistance, and dt is the component of the
direction of tangent of the viscosity resistance.

[0091]Because slipping may exist between the abrasive particle i and the
abrasive particle j when they come into contact, Coulomb's law concerning
slipping is used.

[0092]Normally, where the component of the direction of tangent is greater
than the component of the normal direction, the following occurs:

[et]t=(μ0[en]t/fcoh)sign([et]t)
(7)

[dt]t=0 (8)

[0093]That is, it is the case where the component of the normal is greater
than the component of the component of the direction of the tangent.

[et]t=[et]t-Δt+Δet (9)

[dt]t=Δdt (10)

In equations (7) to (10), μ0 is the coefficient of friction, fech
is the power of adhesion, and sign (Z) refers to positive and negative
signs of the variable Z.Because the abrasive particles to be used in this
embodiment are dry, the power of adhesion between the abrasive particles
may be disregarded.

[0094](4) In step S36, the analysis of the motion equation is executed to
obtain the acceleration expressed by the following equation (11) based on
forces that act on the abrasive particles i and j, which include a force
of the contact and gravity. Further, in this step a similar analysis is
executed for all the abrasive particles,

r = f c m c + g ( 11 ) ##EQU00001##

[0095]where r is the position vector, mc is the mass of the abrasive
particle (it may be obtained by the size and the density in the initial
conditions), fc is the force of the contact, and g is the acceleration
caused by gravity.

Further, a gyration is caused by the angle of the collision when there is
a state of contact. The angular acceleration of it is calculated by the
following equation.

ω . = T c I ( 12 ) ##EQU00002##

where ω is an angular acceleration, Tc is a torque caused by the
contact, and i is an inertia moment.

[0096]The following velocity and the position are obtained after a short
time by the following equations (13), (14), and (15) based on the
acceleration that has been obtained by equation (11). V0 and r0
are the transfer vectors and the position vectors at present. FIG. 13
shows an example of the display of the result of this calculation.

[0097](5) Then a determination whether the position of the blade 13 has
rotated from a given position, e.g., the starting position in the
embodiment, to 270°, is executed (step S37). If not, steps S34 to
S37 are repeated to calculate the angle of the blade, the force of the
contact that acts on the abrasive particles, and the motion equation
obtained after a short time. The calculation is ended when a
determination that the blade turns to a predetermined position is
obtained.

[0098](6) The distribution of the projection with the total and the result
of the calculation of the velocity of the projection are displayed. It
was found that the calculation on the distribution of the projection E1
was close to the real distribution of the projection E, as the results
are similar to those in FIG. 8 in the first embodiment,

[0099]The definitions of the distribution of the projection and the
velocity of the projection from the blade are the following. The
distribution of the projection is described by the histogram of the
direction of the transfer vector of each abrasive particle that is
described by the angle. The velocity of the projection is obtained by
calculating the mean value of the size of the transfer vector. The
variations of the velocity of the projection are obtained by calculating
the standard deviations.

[0100]Sequentially, a test is carried out to see the variation in the
velocity of the projection caused by the outer diameter of the blade. In
the result of a test similar to that shown in FIG. 9, the actual
measurement values were very close to the calculated values (designated
by a broken line).

[0101]This embodiment describes the case where the other movable objects
that should come in contact with each abrasive particle are other
abrasive particles. With the model of analysis of the movement of the
present invention, however, the distribution of the projection and the
velocity of the projection can also be similarly calculated where each
abrasive particle should come in contact with the blade. In this case,
the analysis of the movement of the abrasive particle can be executed by
applying similar steps by replacing the other movable body that should
come in contact with each abrasive particle in the above method with the
blade. Further, the distribution of the projection and the velocity of
the projection can be calculated by using the analytical model of the
movement in consideration of both the contact of each abrasive particle
with other abrasive particles and contact with the blade.

[0102]As another embodiment of the present invention, to be described is a
method for adjusting the distribution of the projection of the abrasive
particle to a predetermined profile. To numerically express the level of
the diffusion of the distribution of the projection, the direction where
each abrasive particle disperses is indicated by an angle. The standard
deviation in the angles of the abrasive particles is assumed to be a
variability of the direction of the abrasive particles.

[0103]In this embodiment, the profile of the distribution of the
projection of the abrasive particles can be adjusted such that the
variability of the frequency to which each discharged abrasive particle
rebounds on blade 13 may come below a predetermined value. To this end,
the size of the blade 13, the range of the positions from which the
abrasive particles are distributed at the opening to discharge the
abrasive particles, and the rate of the rotation of the blade 13, are
configured or combined. This adjustment in the profile of the
distribution of the projection of the abrasive particles can also be
carried out by using the analytical model of the collision of the
abrasive particle and the rotating blade 13 discussed above.

[0104]FIG. 14 shows the relationship between the variability of the
frequencies of the bounces of each abrasive particle and the variability
of the direction of the abrasive particle projection. In this
relationship, the variability of the frequencies of the bounces of each
abrasive particle refers to the standard deviation of the frequencies of
the bounces of each abrasive particle. As will be appreciated from FIG.
14, the variability of the direction of the abrasive particle projection
increases as the variability of the frequencies of the rebounding is
increased. That is, the angle of the projection in the direction of the
projection of the particle diffuses. Therefore, the angle of the
projection can be concentrated by adjusting the variability of the
frequency of the bounces to a predetermined value, for instance, 0.3 or
less.

[0105]FIG. 15 shows a relationship between the mean value of the frequency
of the bounces and the variability of the direction of the abrasive
particle projection. If the mean value of the frequency of the bounces is
less than double, the variability of the abrasive particle discharge
position from the control cage 6 causes the projection angle to be
diffused readily, and then the abrasive particles cannot be accelerated
with stability. Consequently, a variability is caused in the velocity of
the projection. Therefore, it is preferable that the mean value of the
frequency of the bounces be double or more. To change the variability of
the frequency of the bounces and the mean value of the frequency of the
bounces, the outer diameter, the inner diameter, and the rotational
velocity of the blade 13 were changed in the calculations.

[0106]The frequency of splashing greatly affects the factor by which the
distribution of the projection and the velocity are to be decided.
Because the individual abrasive particle splashes several times on the
blade 13, the direction of the projection is turned in the direction of
the rotation of the blade 13 in many splashes. Thus an acceleration by
the collision may be obtained. In contrast, a small number of splashes,
the direction of projection is turned to the opposite direction to the
direction of rotation of the blade 13, and thus the resulting
acceleration is insufficient. Accordingly, combining different
frequencies of the number of splashes of the abrasives causes the
differences in directions of the abrasive particle projection for the
respective abrasive particles, and thus the distribution of the
projection may spread. Therefore, the distribution of the projection of
the abrasive particles can be concentrated by controlling the variability
of the frequency that an individual abrasive particle splashes on the
blade 13 to be a predetermined value or less. On the other hand,
difference number of splashing frequencies to exceed the predetermined
value causes the distribution of the projection of the abrasive particle
to spread.

[0107]FIG. 16 shows the result of the analysis of the distribution of the
projection for a projection experiment under a range (a range of the
discharge) where the abrasive particle discharge position from the
control cage 6 is to be 35° and 10°. As conditions used for
this experiment, the blade 13 has an outer diameter of 360 mm and an
inner diameter of 135 mm, and a rotational velocity was set to 3000 rpm.
As a result, the distribution of the projection was concentrated by the
range of the abrasive particle discharge position being narrow.

[0108]FIG. 17 shows the variability of the direction of the abrasive
particle projection when the range at the abrasive particle discharge
position is changed, under the conditions similar to those in the
experiment of FIG. 16, to see the effect of that range. FIG. 17 indicates
that the variability of the direction of the projection of the abrasive
particle becomes small, and narrows the range at the abrasive particle
discharge position. However, if the range at the abrasive particle
discharge position is narrowed too much, the resistance of the opening 17
of the control cage 6 is increased. This causes problems of decreasing
the possible maximum projection of the centrifugal projection machine and
keeping the abrasive particle in the control cage 6 during the operation.
Preferably, the range at the abrasive particle discharge position is to
be 5° to 20°, to avoid such problems. It was experimentally
found that this range is preferable, regardless of the conditions, i.e.,
the outer diameter, the inner diameter, or the velocity of the rotation
of the blade 13, to be used.

[0109]FIG. 18 shows the relationships between ratios of the outer diameter
to the inner diameter of the blade 13 and the variability of the
direction of the projection of the abrasive particles and of the
frequencies of the rebounding of the abrasive particles. By varying the
ratio of the outer diameter to the inner diameter of the blade 13, the
variability of the frequency of the rebounding is significantly varied,
and thus the variability of the projection direction of the abrasive
particles is also varied. Therefore, the distribution of the projection
can be concentrated by setting the inner diameter and the outer diameter
of the blade 13 to a predetermined ratio. That is, the variability of the
frequency of the rebounding of the abrasive particles becomes 0.3 or less
by setting the ratio of the inner diameter and the outer diameter of the
blade 13 to any of the ranges of 1:1.75 to 1:2.0, 1:2.5 to 1:2.9, or
1:3.6 to 1:4.1. Because these ranges cause that mean value n of the
frequency of the rebounding to become close to the integer, the
variability of the frequency of the rebounding of the abrasive particles
is decreased. The mean value n of the frequency of the rebounding
corresponding to these ranges is near 2, 3, and 4. This is the same as
the case where the range of the ratio of the inner diameter and the outer
diameter of the blade 13 is close to the integer of n=5 or more, although
the range corresponding to n=5 or more is not specified herein in
consideration of the size of the blade actually used. The distribution of
the projection can be diffused by setting the ratio of the inner diameter
and the outer diameter of the blade 13 to be outside these ranges.

[0110]As the conditions of the experiment in this embodiment, the rate of
rotation is 3000 rpm, the range of the abrasive particle discharge
position is 10°, while the outer diameter and the inner diameter
of the blade 13 are varied. Preferably, the rate of rotation is 2500 rpm
or more. If the rate of rotation is less than 2500 rpm, the acceleration
of the abrasive particles is insufficient, and the influence of the
initial velocity of the abrasive particles causes the distance for the
abrasive particles until they collide with the blade 13 to be increased
such that the positions of the abrasive particles are significantly
varied. Therefore, the abrasive particles may be readily distributed on
the blade 13. Thus the variability of the direction of the projection of
the abrasive particle is also increased. Similar to them, the range of
the abrasive particle discharge position is preferably 5° to
20°.

[0111]The respective embodiments just intend to illustrate the present
invention, and are not intended to limit the present invention. For
instance, the projection machine on which the present invention can be
applied is not limited to the centrifugal projection machine as shown in
the embodiments. The present invention can also be applied to a
projection machine that includes a rotary plate that rotates by means of
a driving motor, a plurality of blades mounted on the rotary plate, and a
supply line having an outlet from which abrasive particles are fed to the
blades.

[0112]As the information on the state of projection of the abrasive
particles, although both the distribution of the projection and the
velocity of the projection are obtained in the above embodiments, just
either one of them may be obtained, if desired.

Patent applications by Hiroyasu Makino, Aichi JP

Patent applications by Kyoichi Iwata, Aichi JP

Patent applications by Sintokogio, Ltd.

Patent applications in class MODELING BY MATHEMATICAL EXPRESSION

Patent applications in all subclasses MODELING BY MATHEMATICAL EXPRESSION